We study first structure formation in \Lambda -dominated universes using large cosmological N -body/SPH simulations .
We consider a standard \Lambda CDM model and a \Lambda WDM model in which the mass of the dark matter particles is taken to be m _ { X } = 10 keV .
The linear power spectrum for the \Lambda WDM model has a characteristic cut-off at a wavenumber k = 200 Mpc ^ { -1 } , suppressing the formation of low mass ( < 10 ^ { 6 } M _ { \odot } ) nonlinear objects early on .
The absence of low mass halos in the WDM model makes the formation of primordial gas clouds with molecular hydrogen very inefficient at high redshifts .
The first star-forming gas clouds form at z \approx 21 in the WDM model , considerably later than in the CDM counterpart , and the abundance of these gas clouds differs by an order of magnitude between the two models .
We carry out radiative transfer calculations by embedding massive Population III stars in the gas clouds .
We show that the volume fraction of ionized gas rises up close to 100 % by z = 18 in the CDM case , whereas that of the WDM model remains extremely small at a level of a few percent .
Thus the WDM model with m _ { X } = 10 keV is strongly inconsistent with the observed high optical depth by the WMAP satellite .